A gradian (also called gon) divides a right angle into 100 equal parts, so a full circle is 400 grad. It was introduced for surveying because slopes and right angles become round numbers. It is used mainly in civil engineering and geodesy, particularly in continental Europe.

What is the formula to convert gradians to radians?

Multiply the gradian value by π/200. For example, 100 grad × (π/200) = π/2 ≈ 1.5708 radians (a right angle).

How many gradians are in a full circle?

A full 360° circle equals 400 gradians. A right angle (90°) equals exactly 100 grad, which is one of the key advantages of the gradian system.

How do gradians, degrees, and radians compare?

A right angle is 90 degrees, 100 gradians, or π/2 radians. A full circle is 360 degrees, 400 gradians, or 2π radians. Gradians make right-angle arithmetic convenient; radians are natural for calculus and programming.

Are gradians the same as grades?

Yes — gradian, grade, and gon are all names for the same unit. Scientific calculators often label the mode "GRAD". Do not confuse this with gradient (slope) or the percent grade used for road inclines.

Gradians to Radians Converter

Convert any angle from gradians (grad/gon) to radians using the formula radians = gradians × π/200, with a step-by-step breakdown and common angle reference table.

Enter Angle in Gradians

Gradians (grad / gon)

Common Angle Reference Table

Click any row to load that angle into the converter.

Gradians (grad)	π Form	Radians (decimal)

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Summary

Convert any angle from gradians (grad/gon) to radians using the formula radians = gradians × π/200, with a step-by-step breakdown and common angle reference table.

How it works

Enter an angle in gradians (grad or gon) in the input field.
The converter applies the formula: radians = gradians × (π / 200).
The result is displayed as a decimal and as a multiple of π.
A step-by-step breakdown shows each stage of the calculation.
Click any row in the reference table to load that angle into the converter.

Use cases

Converting gradian angles from surveying equipment to radians for computation.
Checking angle equivalents when working in civil engineering or geodesy.
Understanding the relationship between the gradian and radian systems.
Verifying manual conversions of common right-angle multiples.
Teaching or learning the gradian unit used in European surveying.
Preparing gradian measurements for use in trigonometric functions.

Frequently Asked Questions

Last updated: 2026-09-19 · Reviewed by Nham Vu